Simplify the following expression: $ x = \dfrac{7}{6} - \dfrac{-5k - 2}{k - 6} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 6}{k - 6}$ $ \dfrac{7}{6} \times \dfrac{k - 6}{k - 6} = \dfrac{7k - 42}{6k - 36} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-5k - 2}{k - 6} \times \dfrac{6}{6} = \dfrac{-30k - 12}{6k - 36} $ Therefore $ x = \dfrac{7k - 42}{6k - 36} - \dfrac{-30k - 12}{6k - 36} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{7k - 42 - (-30k - 12) }{6k - 36} $ Distribute the negative sign: $x = \dfrac{7k - 42 + 30k + 12}{6k - 36}$ $x = \dfrac{37k - 30}{6k - 36}$